A Problem with Spitfires

Posted in Cute Problems, History, The Universe and Stuff with tags , , , , , on July 25, 2017 by telescoper

This problem stems from an interesting exchange on Twitter last night, prompted by a tweet from the Reverend Richard Coles:

I think his clerical vocation may be responsible for the spelling mistake. The answer to his question doesn’t require any physics beyond GCSE but it does require data that I didn’t have access to last night.

Here’s a version for you to try at home with all the necessary numbers (though not necessarily in the right units):

A model of a Mark VI Spitfire showing its two 20mm cannons.

A Supermarine  Mark VI (Type 350) Spitfire fighter aircraft weighing 6740 lb is initially travelling at its top speed of 354 mph. The aircraft is armed with two Hispano-Suiza HS.404 20mm cannons, one on each wing, each of which is fed by a drum magazine containing 60 rounds. Each projectile  fired from  the cannon weighs 130 grams, the rate fire of each cannon is 700 rounds per minute and the muzzle velocity of each shell is 860 m/s.

(a) Calculate the reduction in the aircraft’s speed if the pilot fires both cannon simultaneously until the magazines are empty, if the pilot does nothing to compensate for the recoil. Express your answer in kilometres per hour.

(b) Calculate the average deceleration of the aircraft while the cannons are being fired, and express your result as a fraction of g, the acceleration due to gravity at the Earth’s surface which you can take to be 9.8 ms-2.

(c) A Mark 24 Spitfire – which is somewhat heavier than the Mark VI, at 9,900 lb (4,490 kg) – is armed with 4×20mm cannons, two on each wing. The inboard cannon on each wing has a magazine containing 175 rounds; the outboard one has 150 rounds to fire. Repeat the above  analysis for these new parameters and comment on your  answer.

Answers through the comments box please!




Deep Time and Doggerland

Posted in Biographical, Music, The Universe and Stuff with tags , , , , , on July 24, 2017 by telescoper

One of the bonuses on offer during the BBC Proms season on Radio 3 is the opportunity to listen to the fascinating discussions recorded over the road from the Albert Hall at Imperial College and broadcast during the intervals under the title of Proms Extra. Last week (at Prom Number 4) there was a discussion with the title Deep Time, taking its theme from the UK premier of a fascinating composition of the same name by Sir Harrison Birtwistle.

The Proms Extra programme focussed on `Deep Time’ in the sense in which it is used in geological, i.e. time as inferred from rock strata and the fossil record. In the course of the discussion mention was made of Doggerland which is not, as you might imagine, a theme park devoted to outdoor sexual activities, but an area now submerged beneath the North Sea that connected Great Britain to continental Europe during and after the last glacial period. About 12,000 years ago at the start of the Holocene Era, it is thought that the area now covered by the North Sea looked something like this:

(Picture credit: this website). Obviously the cities marked on the map where not there at the time! Britain was connected to mainland at this time, although much of the land mass was under glaciers at the time. At the end of the last ice age the glaciers retreated, sea levels rose and the area once covered by Doggerland was submerged. It is thought that this happened around 8500 years ago. Great Britain has been separated from the continent by less than 10,000 years.

Doggerland gets its name from the Dogger Bank, a huge sandbank off the North-Eastern coast of England which is thought to be a glacial moraine left behind by the retreating ice sheet. The Dogger bank lies about 60 miles from the coast, and is about 60 miles wide by 100 miles long. The water is quite shallow – typically 20 metres deep and is a well-known fishing area. Its name derives from old Dutch fishing vessels called doggers who specialised in catching cod. Here’s a map (from here) showing the Dogger Bank:

When I was a teenager I had the opportunity, with a few friends from school, to go out from Newcastle in a trawler to the Dogger Bank. The skipper insisted that the Dogger Bank was, in places, so shallow that you could paddle around on it with your trousers rolled up. We all believed him, but he was clearly having us on!

The other thing I remember about that trip in a trawler – apart from the all-pervasive smell of fish – was that a bit of storm brewed up on the way home. All my school friends got sea-sick, but I didn’t. That was the first time I realised that I don’t suffer from seasickness. I can enjoy travelling on ships and boats without having to worry about it.

Dogger is of course also the name of one of the sea areas used in the Shipping Forecast: it is East of the coastal area Tyne, South of Forties, North of Humber and West of German Bight. Whenever I hear the shipping forecast on the radio, I always feel a bit of nostalgia when I hear the names of these areas read out.

Anyway, trawlers operating at the Dogger Bank frequently bring up bits of ancient animals (including mammoth and rhinoceros) as well as prehistoric human artefacts, showing that the area was at one time inhabited. I don’t think anybody knows exactly how long it took Doggerland to become submerged, but it may well have involved one or more catastrophic flooding events. If there were people living on Doggerland then,  they obviously had to migrate one way or the other..



Women’s Cricket World Cup Winners!

Posted in Cricket on July 23, 2017 by telescoper

There wasn’t any cricket in Cardiff today because  Glamorgan’s T20 Blast match was abandoned without a ball being bowled. However, that meant I was able to follow the thrilling final of the Women’s World Cup at Lord’s, which was won by England by 9 runs.

I didn’t think England’s total of 228/7 off 50 overs was going to be enough, and India seemed to be set for a comfortable win, but England’s bowlers stuck to their task magnificently and India crumbled in the last five overs to be bowled out for 219, having lost their last 6 wickets for just 24 runs.

A great performance by England and a magnificent advertisement for Women’s Cricket in front of a sellout crowd at Lord’s. I think this may herald a huge surge in popularity for the women’s game. Congratulations to England and commiserations to India.

Now, is there anything to stop England fielding an all-female team against South Africa on Thursday? England women played with a lot more determination today than the men did against South Africa at Trento Bridge!

The Brexit HBR Business Case

Posted in Uncategorized on July 23, 2017 by telescoper

I think the Government has picked option C!

Voice of TREASON


Today we’re going to work through a strategic business case to evaluate how you’re likely to perform in role.

Investment Case

You have an initial investment of £50-60B to make that will have an impact in £100s of Billions over decades. The transformation will completely distract your Executive Team and all your senior managers leaving you unable to do anything else except the project. Once initiated the project cost will be sunk and and the company irreversibly comitted to the course.

All of your consultants have advised you against initiating the project. Your competitors, sensing a misstep have started to hire your most trusted staff. You have a tenuous grip on your board and e-team and expect to lose some critical board votes that will secure the project.

You’re  certain you don’t have the staff to manage the initial analysis  let alone the deployment of the project.

A year ago…

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Natwest T20 Blast: Glamorgan v Sussex

Posted in Cricket with tags , , , on July 22, 2017 by telescoper

Last night’s Twenty20 match in Cardiff was planned as a staff social outing for members of the School of Physics & Astronomy at Cardiff University. I had to do some things at home before the 6.30 start so didn’t join the group that went to a pub first but went straight to the ground.

It had rained much of the day, but stopped around 6pm. When I got to the ground the covers were still on:

The umpires inspected the pitch at 7pm, and during their deliberations it started drizzling. They decided to have another look at 7.30.

I stayed inches ground, updating the rest of the staff group who happily stayed in the pub while I sat in the gloom of a sparsely populated SWALEC.

Eventually the ground staff started to remove the covers

The toss was finally thrown at 8pm. Glamorgan won and decided to field. Play would start at 8.30, with 9 overs per side.

Play did get under way at 8.30..

It was predictably knockabout stuff, with Sussex slogging from the word go. They reached 87 for 2 off 8 overs, but then the rain returned. A little after 9pm the game was abandoned. Fewer than 10 overs having been bowled, tickets were refunded.

It was a shame that we didn’t get a full game, not only because the social event was a damp squib, but also because Glamorgan really wanted a win. Their previous match at the SWALEC (against Somerset last Saturday) was also rained off but their match  the following day against Essex in Chelmsford led to a victory with a six off the last ball as Glamorgan chased 220 to win off 20 overs.

Anyway, it’s the return match against Essex in Cardiff on Sunday so let’s hope for a full game then.

The Dead Statesman

Posted in Poetry, Politics with tags , , on July 21, 2017 by telescoper

I could not dig; I dared not rob:
Therefore I lied to please the mob.
Now all my lies are proved untrue
And I must face the men I slew.
What tale shall serve me here among
Mine angry and defrauded young?

by Rudyard Kipling (1865-1936)

A Problem of Brightness

Posted in Cute Problems with tags on July 20, 2017 by telescoper

It’s been a while since I posted anything in the Cute Problems folder, so here’s a nice one:

Two physics students are studying at desks in the same room. The two outlets of the wall socket to which their desk lamps are attached have inadvertently been wired in series rather than in parallel. The only bulbs available for the lamps are designed for the nominal mains voltage (240V) : Student A chooses a 200W bulb for his lamp; Student B opts for a 50W bulb for hers.

Which is the brighter student?

Hint: Assume that the filament in each bulb obeys Ohm’s Law.

Answers through the comments box please, preferably with working…..